The way I interpreted it was: It became so urgent for him to secure Caloris's future that he couldn't put it off any longer. In the aftermath of the earthquake, it's mentioned that Caloris was the hardest-hit region, with monsters escaping the Old Forest and slaughtering whole villages. It's so bad that the epilogue states that Caloris peasants protest during the coronation and Joslyn is forced to leave the celebrations early and return to his duties.

By default, Joslyn won't remarry. However, if marriage becomes a hot subject among the nobility (by Elodie or Brin getting engaged in the first half of the game), his statements about Sirin suggest that he's also feeling the pressure of having to produce an heir; and thus he ends up marrying her if she wasn't successfully chased off. The marriage with Brin is prompted by a whole different motivation, but it's still pairing together two people who'd otherwise have trouble producing heirs.

My theory is that with Caloris in full crisis mode, he's under immense pressure to do damage control in his duchy, especially since he's been absent for the past 40 weeks and it was his own daughter that contributed to his mess. Marrying and providing a Caloris heir may have been part of ensuring stability - what would have happened if he was killed in the chaos while both he and Armand were still heirless?

Why that specific earl's daughter, I think can only be speculated at. It seems like she's too far down the line to inherit, so maybe her lack of titles to pass on was a factor. (Less titles = less kids = less trying to conceive those kids!) Or maybe he just wants to avoid any political shenanigans and marry someone from a relatively unimportant family. Whatever the case, he settles down as fast as possible and, luckily, gets an heir out of it very quickly. That's one less thing for Caloris to worry about, during a time of great fear and turmoil.